Calculating risk using max loss and asset correlations

CFA Level III Derivatives
#1

I trade virtuals in the energy market and have challenged myself to calculate VAR more appropriately. Our current VAR calculation is purely historical and uses the worst two-day performance of the multi-asset portfolio. However, I don’t believe this accurately accounts for the potential two-day risk of the portfolio. The portfolio consists of several different spreads, or assets, if you will, which on any given day could “blow up.” Even though two assets may not have endured significant losses on the same day in the past, their 0.60 correlation suggests they could in the future. My current model doesn’t take this into account.

I’d like to develop a model (potentially Monte Carlo) whose inputs are the individual assets’ two-day loss and the covariance between the assets which would be run to simulate potential outcomes. Any ideas on the best approach? Keep in mind I’m not using the assets’ expected value or standard deviations, but their worst losses and covariances.

#2

I am obviously no expert on this but have you thought of using copulas to model this 0.6 dependency? what you could perhaps do is model the joint distribution of asset returns by fitting or constructing an appropriate copula, you could then simulate portfolio returns from this joint distribution and calculate the VaR. This VaR measure should incorporate the correlation between assets ?

Not sure if this helps,especially if we are talking about a two day loss.

But meh !

#3

Interesting. Although I had never even heard of copulas, a quick google search suggests this has some promise. Thanks.

#4

I dont know a thing about the underlying maths but the concept does seem quite prevalent in risk management. There is an excel addin…never tried it out so cant say about quality but the website seems quite intuitive

http://www.hoadley.net/options/develtoolscopulas.htm

#5

workdog,

I did some Monte-Carlo work a couple of years ago simulating a portfolio of stocks. This included taking into account the price movement correlations of the stocks in the portfolio.

I found the willmot.com forum to be really helpful to figure out how to put this thing together.

I have my original spreadsheet that I built as well that I’d be happy to shoot you if you’re interested. Just email me. I’ll try to dig it up and send it to you.

#6

Thanks, Clever. Email coming.

#7

We often just assume that correlations go to 1 and see what that does to portfolio risk. It doesn’t fully fit into a VaR definition, but it has the advantage of being computationally simple and fitting the fact that correlations get very high in true crisis events.